How do we establish causation?

Ross Pomeroy at Real Clear Science discusses five logical fallacies that often get misidentified and abused in arguments. Identified by Steven Novella in his book The Skeptic’s Guide to the Universe, one of these is the old Correlation and Causation fallacy:

2. Correlation and Causation. Correlation does not prove causation. To say that it does is a logical fallacy. However, correlation absolutely can be evidencefor causation, the quality of which depends upon, for example, whether the correlation is actually feasible, how strong studies show the link to be (effect size), and whether or not the variables in question demonstrate a dose response (if X fluctuates, does Y also change in a predictable way?)

I often see this one expressed as, “Correlation does not imply causation,” which I think is wrong. As Pomeroy is careful to stipulate, correlation does imply causation. It just doesn’t, by itself, prove it.

But the question is, what does demonstrate causation? David Hume pointed out that we never observe causation, ever. We only ever observe correlation. (Which is related to the infamous problem of induction.) We can only infer causation. But then how do we discriminate between a scenario where two variables are merely correlated from one where one factor causes another?

Pomeroy above talks about whether the variables in question fluctuate together, and I think that’s usually a promising sign, but not always. I know in troubleshooting IT systems, I’ve encountered situations where two variables did fluctuate together but were actually both caused by a third variable that was later uncovered.

So then what tells us that one thing causes another? I think the answer is that we have to isolate the correlation down to one essential item that, if missing, the effect doesn’t occur.

So when establishing a link between, say, an increase in occurrences of a disease and a certain lifestyle or dietary choice, the statistical increase in the occurrence of the disease has to be isolated to one necessary and sufficient factor, with all other factors, such as genetics, eliminated or controlled for. It’s why we can say that smoking causes lung cancer, but have no grounds to say that artificial sweeteners cause cancer.

But is that right? Are there other criteria we should bring to this? How do we know when we’ve found a true cause?

35 thoughts on “How do we establish causation?”

Take cholera for example (https://en.wikipedia.org/wiki/Cholera). We know we have found its true cause when we have identified the bacterium Vibrio cholerae, its occurrence in the environment, its life cycle, the way it enters the human body, and the way it acts when it attaches to the intestinal wall. Once those things are known everything that was regarded as mere correlations–symptoms, food consumed, sanitation, poverty, effective treatments, etc.–falls into place.

I think we are forced to rely on statistical correlations when we don’t know the particular mechanisms by which nature operates. Once we learn those mechanisms the issue of “correlation vs causation” disappears.

I definitely agree that knowing a lower level mechanism for a higher level correlation helps. But when you get down to it, what is a mechanism but a sequence of well known correlations? A billiard ball striking another certainly seems like a straightforward mechanism for moving the second ball, but that’s only because we’ve become very familiar with that correlation and the associated theory (Newton’s laws) about what happens.

(Although some correlation happen so often in nature that we’ve probably evolved innate intuitions about them. Babies notice when physically impossible things appear to happen.)

Beat me to the punch on this one. I’ll finish what I’m working on …
All theories are bound to be a little off. They wouldn’t be at all useful otherwise.
I’m not sure that we want causality to mean mere necessity without sufficiency, as mentioned below. That leads explanation pretty far afield.

Good point. All theories are predictive models, with varying levels of accuracy. A theory that isn’t 100% accurate (and as you note, none are, although some come close within certain domains) is still useful. Today we know that Newton’s laws aren’t as accurate as General Relativity, but Newton’s theory is a lot easier to work with, and it gets us to the moon. (Although precisely syncing time with spacecraft and satellites requires GR.)

The only precise theory would be, to coin a phrase, “It is what it is.”
And of course, that is not a theory at all; it is the one and only truism (and trending cliché). What use is that statement?
We get confused because, to become useful, the theory of logic takes off from that statement with an instance to type equivocation.
That little trip then leads to a tumble into a wonderland of cats on mats, barn facades in the distance, and on and on.

“A billiard ball striking another certainly seems like a straightforward mechanism for moving the second ball…”

Not so. The mechanism involved seems like what Richard Feynman described in Volume 1 of his Lectures on Physics (38-6):

“So we now understand why we do not fall through the floor. As we walk our shoes with their masses of atoms push against the floor with its masses of atoms. In order to squash the masses of atoms closer together, the electrons would be confined to a smaller space and, by the uncertainty principle, their momentum would have to be higher on the average, and that means high energy; the resistance to atomic compression is a quantum-mechanical effect and not a classical effect.”

I was thinking along the same lines as Mark Titus, above: It’s when we understand the mechanism behind the correlation. (In your IT situation, it’s when you understood the mechanism — what was really broken — that the causation became clear.)

“I think the answer is that we have to isolate the correlation down to one essential item that, if missing, the effect doesn’t occur.”

Agreed. If it can be shown an effect is contingent on a cause, that seems pretty strong evidence.

Over 90% of all people in prison ate carrots and peas as a child! Is that a cause and an effect? If so, you have to show how. We now know that the sun doesn’t come up in the morning. The earth rotates on its axis (west to east here) and the sun springs into view every day. It is a nice hypothesis but is it cause and effect? The idea makes sense, if the Earth did rotate from west to east then the sun would “rise” in the east and “set” in the west. But can we show that the earth is rotating? The answer is yes, there is scads of evidence for that and, in addition we have scads of other information regarding the masses of both Earth and Sun and there is no way the much more massive sun could be rotating around the tinier Earth at such a speed.

So, all such “cause and effect” chains are provisional. The evidence in support must be weighed and a mechanism must be established that links cause to effect. This is where so many claims about our health (inoculations, effects of radiation, environmental chemicals, etc.) come acropper because such a link doesn’t get proved. It wasn’t long ago that we finally figured out how aspirin works. So, many “health issues” sit in a “very provisional” state for a long time. But we want certainty, so we claim causes and effects.

I think the main thing to remember is that we never escape a proposition being provisional. We can decrease the uncertainty to lower and lower levels with further investigation, but we never reach zero. A black swan can always come along and throw a monkey wrench into what think is established science.

Sorry to be nit picky here Mike, but you are using “imply” in the colloquial sense (“Are you implying that I look fat?”) as opposed to the mathematical/logical sense: p -> q = “p implies q” = “if p, then q”. Given this is actually a mathematical/statistical question, I would say correlation can suggest causation, or afford causation, instead of implies causation.

As for the main question of the OP, this is an entire field of endeavor, and if you want to dive in I highly (Highly, HIGHLY) recommend starting with Judea Pearl’s “The Book of Why”. I have not taken the time to completely understand it, but his take “feels” right to me.

The interesting (to me) angle on this is figuring out exactly how we humans actually learn to intuit causality, because then we should be able to provide that capability to artificial intelligence, and then bang!

James,
On “imply”, I don’t know. I just skimmed some definitions at the usual internet dictionaries, and they all seem to be related to suggesting or hinting at something rather than an iron clad consequence. It might be that in strict logician language it does mean that, but the common usage seems so pervasive now that anyone using it in the stricter sense has a responsibility to clarify the specialty version they’re using.

Thanks for the book recommendation. If this becomes a burning question I must explore, I’ll definitely check it out.

One point that perhaps should be made is that the concept of causation is a human construct and not necessarily something objectively out there in the natural world, so searching for a very robust definition of and criteria for causation may be a wild goose chase.

Or maybe not.

In any case, there are two issues here which need to be considered separately. The first is what do we mean by a cause, and the second is how can we distinguish causes from mere correlates.

I guess James is right that there must be a substantial philosophical body of work on both questions, and I’m not familiar with it. Off the top of my head, I’d approach them as follows.

For the first question, for X to be a sole cause of Y, X has to be something contingent that we can turn on or off in repeated experiments (or at least imagine being different in other possible worlds, with all else being equal). If X is always followed by Y, and the absence of X is never followed by Y, then X is a cause of Y.

This scenario can be distinguished from mere correlation because we are toggling X on and off (or stipulating that it does or doesn’t happen, with all else being the same). X is under control, and by dint of controlling X we also control Y. Conversely, intervening somehow to prevent Y does not affect X, so Y is not a cause of X. We can rule out the possibility of a third variable intervening because we’re not changing anything else.

If X merely increases the likelihood of Y in these circumstances, then it isn’t really a sole cause but a contributing factor. In the real world, there are few such sole causes, and such ideal sole causes perhaps don’t exist at all. In this view, smoking doesn’t cause cancer, it is a contributing factor, so the idea of a “true cause” is perhaps a red herring.

The epistemic question is never going to be so clean, and its hard or impossible to eliminate all uncertainty. It’s always going to be something of an inductive process. You’re going to have to try to reproduce the ideal circumstances of the definition somehow by eliminating all confounding factors, and that ain’t easy.

I should have been more precise in my language, that smoking increases the probability of getting lung cancer. You can get it despite never smoking, and you can smoke and never get it, but if you smoke, the chances of getting it are dramatically higher.

Well said all around. I agree. The point about causation being a human construct is interesting. Like you, I sometimes have that suspicion, but also am not really sure. It’s also possible that causality is out there, but is emergent from quantum phenomena. (Granted, with the right interpretation of QM, this isn’t true.)

Yeah, I should have clarified that I think your original article is spot on, and I think we are mostly on the same page.

You know I’m a proponent of the MUH, and sorry to bring it back to that again, but something I have seen as an argument against the MUH is that there’s no causality in mathematics. Everything just is. So therefore the physical world cannot be a mathematical object.

That’s why it’s important for me to make the point that causality is a human construct rather than something out there, or at least that there is causality in the real world only insofar as there is causality in a mathematical world like that of Conway’s Life.

I know you’re skeptical of the MUH, but perhaps we can agree on this much?

Hi DM,
No worries on bringing up the MUH. Lots of people here regularly bring up their favorite theories or outlooks.

On causality being a human construct, I’m not sure. Depending on which interpretation of quantum mechanics we favor, it might be an emergent phenomenon. It does seem like a crucial concept for understanding the classical world. But I could see the argument that it’s a matter of perspective from the inside of a static unchanging 4+ dimensional structure.

Of course, strictly speaking the concept is a human construct, just like any theory is, but looking at it that way sweeps a lot of things under the human construct carpet. Ultimately the question is whether the theory of causality is predictive in the sense that everything should have a cause, and at least at classical levels, it appears to be.

Also, I think one of the major problems with understanding causality is the concept of “cause and effect”. Treating a “cause” as a thing and not a process creates confusion. The noun form would be better as “causation”. For myself, I have benefited from modeling causation as:
Input -> [context or mechanism] -> Output,
and saying the mechanism (or context) causes the output when presented with the input. Just referring to “cause and effect” ends up conflating the input and the mechanism as the “cause”.

I can point out that Aristotle had it right with his 4 causes, except I wouldn’t uses “causes”. I would say any specific causation has either 3 or 4 attributes, namely, the material (input), efficient (mechanism), formal (output), and sometimes final (purpose).

There are many things people refer to as a noun that are processes (causation, consciousness, awareness, photosynthesis, etc). Although if you think about it, everything ultimately is a process. Even elementary particles are really just excitations of quantum fields.

Corresponding to the Immortal Principle, which is an architecture grounded in strict monism, cause and effect are one and the same. In laymen terms, only one “thing” is responsible for motion and form, and that one “thing” includes both motion and form. In this paradigm, the cause “is” always the effect which coalesces into the diversity and novelty of expression. The “hard problem of causation” runs on a parallel track with the “hard problem of consciousness” both of which are stymied by the meta-problem. Good luck…

In the realm of philosophy, you can argue back and forth about what’s a true cause but, in the real world of IT, we called it the “root cause” which, although sometimes elusive in the instantiation of it, was crystal clear about what defines it: that element or event that, when present, a problem symptom appears, and when absent, that symptom does not appear. There are two useful rules of thumb in this regard: (1) the Black Cat Hypothesis: the last event that occurred just before the problem symptom appeared is a likely candidate cause; and (2) Occam’s Razor: [although it’s theoretically possible that two or more elements or events caused the problem symptom,] the law of parsimony states that simpler solutions are more likely to be correct than complex ones.

The Black Cat Hypothesis is a catchy name. We usually look for what the last change was, what’s different from the previous (presumably) successful cycles. I say “presumably” because I’ve seen two bugs counteract each other before until one was fixed, revealing the existence of the other one.

On causality, my go-to source is Judea Pearl, Causality: Models, Reasoning, and Inference. The book caused something of a revolution in the social sciences and medicine, and none too soon. It models causal relations with directed acyclic graphs, and integrates these graphical models with a Bayesian framework.

The “acyclic” part means that if A causes B causes C, we don’t also have C causes A. So right there, we have something more than correlations, which are always bidirectional. Pearl uses the concept of an “intervention” which is an event from outside a system of interest, which sets the value of a given variable.

I like your suggestion for deciding that one thing probably causes another Mike, or “isolate the correlation down to one essential item that, if missing, the effect doesn’t occur”. While not some kind of absolute determination, this does seem to be a useful heuristic in general. It’s an effective reduction. In order to promote more of what we want, as well as restrict more of what we don’t want, it should be helpful to understand associated causes. As you know, I’m very much into causality.

My epistemology doesn’t address causality specifically, though my metaphysics does (as in without causality there’s nothing to figure out anyway). But it does suggest that if things do exist to epistemologically figure out, then they must function by means of causally. So then how might causality itself be assessed?

Well my EP2 does actually make it there, though in a big picture way. Here any model becomes more believed as it remains consistent with evidence, and a model might involve the determination of causality. But what if a person has use for a more compact rule regarding nothing more than causality itself? What might we tell the kids (and yes, ourselves)? In that case we could suggest a Mike Smith rule:

“Causation may effectively be presumed when a correlation is isolated down to one essential item that, if missing, the effect doesn’t occur.”

It’s a parsimonious definition, given that smoking would not by itself “cause” lung cancer, though I see this as a strength.

I think it is possible for some things to have a combination of causes, so the one thing rule isn’t iron clad. Although in practice, things with multiple causes tend to be complex composite phenomena whose individual pieces have single causes, so it definitely seems like the exception rather than the rule. In any case, the trick seems to be to isolate the minimum number of factors that, if present, the observed correlation happens, but if absent, it doesn’t.

That said, before we go naming any rules after me, we’d probably want to read the books suggested by Judea Pearl that James and Paul suggested. I’m pretty sure someone else already deserves to have their name on it 🙂

Oh, and on the Big Think piece about Einstein, did you catch the part about Bohr and Heisenberg’s anti-realist (instrumental) stance? As I said before, I do think Bohr crossed the realist line at times in his debates with Einstein, but really the difference between them was whether a purely instrumental (useful) scientific theory was sufficient or that it wouldn’t be complete until there was a realist interpretation. (I wonder how Einstein would have felt about the Everettian interpretation.)

Sorry Mike, but my way sounds much more fun! Henceforth, I shall refer to this as your rule, that is until I’m informed that it’s actually the intellectual property of another. And in that case, trust that I’ll provide this person a heartfelt “Sorry, my bad”. There’s obviously no plagiarism element to be concerned about here, so why not? Furthermore we’ve got plenty of highly educated friends around these parts who’ve read all sorts of books and articles over the years. If any of them fail to provide a better attribution for your causation rule, then it might be because there are none to be found.

But wait a minute, you’ve now provided an improvement:

“Causation may effectively be presumed when a correlation is isolated down to isolate the minimum number of factors that if present the observed correlation happens, but if absent it doesn’t.”

Well done sir! You seem to have now “beaten cancer” (which is to say, found a way for apparent causality to include my smoking/ lung cancer scenario).

A few years ago over at Massimo’s it was this “take it or leave it” route that I used when I began quoting my four principles of philosophy. On my EP2, initially a distinguished philosophy professor claimed “I can think of lots of other ways to figure something out,” but when inquirered he failed to provide any such example. At this point in the game I’m pretty sure that no one is going to take my four principles away from me.

In truth however I’d love it if one or more prominent persons were to either discover them independently, or even take the route of plagiary. I didn’t develop these principles for their own sake, but rather so that I might better found my ideas. The more that science and philosophy take this path, the better that things should be for me regardless of who takes credit for what.

Thanks for noting the instrumentalism of Bohr and Heisenberg when compared against Einstein’s apparent realism. Right. It was probably the debate itself that goaded Bohr into a realist slot. And look, Einstein was no true philosopher. He was an explorer of reality who was utterly offended by supernatural interpretations of physics. I was struck quite the same when my professors fed me the contradictory term “natural uncertainty”. It was like they were telling us “Okay students, the virgin has once again become pregnant”! But I wish that I could go back in time to modify Einstein’s statement to something more along the lines of “To the extent that God plays dice, nothing exists for us physicists to understand.” Then he could have kept his instrumentalism, as well as remained the worlds greatest proponent for naturalism.

Your smoking causes lung cancer example (although I do believe it):
Smoking does not always lead to lung cancer – hence it is not a sufficient condition.
Lung cancer does not always occur in smokers – hence it is not a neccessary condition either.

I was sloppy with the language there. What I should have written is that smoking increases the probability of getting lung cancer. In that particular case, we can only isolate the correlation across populations of subjects.